The present two-component model provides insight into superconducting properties of systems with several components and should be investigated prior to development of more sophisticated models.
The Fermi momenta of protons and neutrons are very different as a result of nuclear equilibrium [1]}.
The order parameter is diagonal in the isospin quantum number because particles with significantly different Fermi momenta cannot form a Cooper pair with zero total momentum.
Some aspects of the two-component GL model in the context of the NS matter were studied earlier [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}.
The vector coupling of the SF components was represented in the free energy functional by "current \(\cdot \)  current" terms [2]}, [8]} or by "SF density gradient \(\cdot \)  SF density gradient" contributions [7]}, [9]}.
Here, both types of coupling are retained and are called simply "momentum-coupling" and "gradient-coupling", correspondingly.
It is convenient to introduce a shorthand term "density-coupling" that refers to the SF-SC density-density coupling between the protons and neutrons.
In this paper, a novel SF interaction is considered in the form of a "gradient of wave function modulus \(\cdot \)  gradient of wave function modulus", which represents a mixed quantum pressure contribution.
